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Instructor: Profs. Paul Avery, Selman Hershfield
PHYSICS DEPARTMENT
PHY 2049
Exam 2
March 1, 2011
Name (print, last first):
Signature:
On my honor, I have neither given nor received unauthorized aid on this examination.
YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE.
DIRECTIONS
(1) Code your test number on your answer sheet (use 76–80 for the 5-digit number). Code your name on your
answer sheet. DARKEN CIRCLES COMPLETELY. Code your student number on your answer sheet.
(2) Print your name on this sheet and sign it also.
(3) Do all scratch work anywhere on this exam that you like. At the end of the test, this exam printout is to be turned in.
No credit will be given without both answer sheet and printout with scratch work most questions demand.
(4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do not
make any stray marks or the answer sheet may not read properly.
(5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing.
>>>>>>>>WHEN YOU FINISH <<<<<<<<
Hand in the answer sheet separately.
Constants: e = 1.6 × 10−19 C
mp = 1.67 × 10−27 kg
me = 9.1 × 10−31 kg
²o = 8.85 × 10−12 C 2 /N · m2
k = 1/(4π²o ) = 9 × 109 N · m2 /C 2
g = 9.8m/s2
µo = 4π × 10−7 T · m/A
micro = 10−6
nano = 10−9
|q1 ||q2 |
Coulomb’s Law: |F~ | =
(point charge)
4π²o r2
~
~ =F
Electric field: E
q
~ =
E
~A=
Gauss’ law: Φ = n̂ · E
H
pico = 10−12
q
r̂ (point charge)
4π²o r2
~ dA =
n̂ · E
~ =
E
R
dq
r̂ (general)
4π²o r2
E=
σ
(plane)
2²o
qenc
²o
R
1
1
F~ · d~s = mvf2 − mvi2 = Kf − Ki
P = F~ · ~v (mechanical power)
2
2
R
For conservative forces Uf − Ui = − F~ · d~s → Ki + Ui = Kf + Uf
Energy: W =
Electric potential: V =
Vb − Va = −
Rb
a
U
q
Ex dx = −
Capacitors: q = CV
Rb
a
u=
R=
q = CV (1 − e−t/RC ) (charging)
~
Magnetism: F~ = q~v × B
~ =
dB
µo id~s × r̂
4π r2
H
Ex = −
∂V
,
∂x
K²o A
(parallel-plate)
d
q2
2C
dq
= jA
dt
q
(point charge)
4π²o r
~ · d~s
E
C=
U=
Resistors: i =
V =
1
²o E 2
2
V
i
V =
Ey = −
∂V
,
∂y
Ez = −
∂V
∂z
C = C1 + C2 (parallel)
ρL
(wire)
A
P = iV
q = qo e−t/RC (discharging)
~ · d~s = µo ienc
B
dq
(general)
4π²o r
1
1
1
=
+
(series)
C
C1
C2
R=
~ ×B
~
F~ = iL
R
µ = N iA
B=
R = R1 + R2 (series)
1
1
1
=
+
(parallel)
R
R1
R2
~
~τ = µ
~ ×B
~
U = −~
µ·B
µo i1 i2
F
=
l
2πr
µo i
µo i
µo iN
, (wire)
(loop center),
(solenoid)
2πR
2R
L
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1. A current carrying square loop of wire is placed in a uniform magnetic field
pointing to the right (see figure). If the magnetic moment is is pointing up,
what is the direction of the current flow in the wire segment closest to you
labeled by i in the figure and which direction will the loop rotate (clockwise
or counterclockwise)?
(1)
(2)
(3)
(4)
(5)
i to the left; rotate clockwise
i to the right; rotate clockwise
i to the left; rotate counterclockwise
i to the right; rotate counterclockwise
There is no torque on the loop.
2. Each of the wires in the figure carries a current of 1 A perpendicular to the
page
with the direction of current flow indicated. For the path shown, what is
H
~
B · d~s.
(1)
(2)
(3)
(4)
(5)
2.5 × 10−6 T · m
3.8 × 10−6 T · m
−2.5 × 10−6 T · m
1.3 × 10−6 T · m
−3.8 × 10−6 T · m
3. The three light bulbs in the Figure are identical. If the brightness or power of
bulb B is P , what is the brightness or power of bulb A?
A
C
B
(1) P
(2) 4P
(3) P/2
(4) P/4
(5) 2P
10Ω
4. In the figure shown, what is the current through the 5Ω resistor?
(1)
(2)
(3)
(4)
(5)
3Ω
+
2.0 A
0.5 A
0A
1.5 A
1.0 A
8V
2Ω
+ 5V
3V
+
10Ω
5. Four wires each have current i flowing perpendicular to the corners of a square
with the directions indicated in the figure. What is the direction of the magnetic field at the center of the square (point P)?
(1) î
(2) k̂
(3) −ĵ
(4) −î
6. Charges Q1 > 0 and Q2 < 0 have velocities in the plane of the page as indicated
in the figure. A uniform magnetic field with magnitude B is going into the plane
of the page, and a uniform electric field with magnitude E is going up (towards
the top of the page). If the speed of charge 1 satisfies v1 > E/B and the speed
of charge 2 satisfies v2 < E/B, what is the direction of the net force on charges
1 and 2? (Up means towards the top of the page, and down means toward the
bottom of the page.)
(1)
(2)
(3)
(4)
(5)
The
The
The
The
The
net
net
net
net
net
force
force
force
force
force
on both particles is up.
on both particles is going into the page.
on both particles is down.
is down on Q1 and up on Q2 .
is up on Q1 and down on Q2 .
(5) ĵ
5Ω
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7. A wire is 2.0 m long and 0.564 mm in radius. When connected to a potential difference of 2.0 V, a current of 4.0 A flows
in the wire. The resistivity of the wire is:
(1) 2.0 × 10−7 Ω·m
(2) 2.5 × 10−7 Ω·m
(3) 1.0 × 10−7 Ω·m
(4) 4.0 × 10−7 Ω·m
(5) 0.5 × 10−7 Ω·m
8. The light bulbs A and B in the circuit shown are identical. When the switch
S is closed, what happens to the brightness or power of the light bulbs?
(1)
(2)
(3)
(4)
(5)
A
12 V
B
18 V
S
Nothing changes
A gets brighter, B dimmer
A gets dimmer, B dimmer
A gets brighter, B brighter
B gets brighter, A dimmer
18 V
9. The current density inside a long, solid, cylindrical wire of radius a = 2 mm is in the direction of the central axis and
its magnitude varies with radial distance according to J = Jo (r/a)2 , where Jo = 300A/m2 . What is the magnitude of
the magnetic field at a distance r = 1 mm from the center?
(1) 9.6 × 10−8 T
(2) 2.4 × 10−8 T
(3) 3.0 × 10−8 T
(4) 7.2 × 10−8 T
(5) 4.8 × 10−8 T
10. All capacitors are 18 µF in the figure. What is the equivalent capacitance
between points A and B?
(1)
(2)
(3)
(4)
(5)
18.0
45.0
54.0
28.5
36.0
µF
µF
µF
µF
µF
A
B
11. A 12 V battery is connected to a capacitor with 2.0 cm×2.0 cm parallel plates, separated by a 0.1 mm air gap. While the
capacitor is connected to the circuit, the space between the plates is filled with a dielectric slab with dielectric constant
4.5. How much does the charge on the positive plate change (in nano-coulombs) after the dielectric is added?
(1) −0.43
(2) +1.9
(3) −0.33
(4) 0
(5) +1.5
12. A closed current path is made from two different circular arcs as shown in the
figure. The larger arc has radius 3 cm and covers one quarter of the circle, and
the smaller arc has radius 1 cm and overs the remaining three quarters of the
circle. If the current is 1.5 A going clockwise, what is the magnetic field at the
center of the circular arcs?
(1) 79 µT into page
(2) 63 µT into page
(3) 63 µT out of page
(4) 71 µT into page
(5) 79 µT out of page
13. Pulling the plates of an isolated charged capacitor apart:
(1)
(2)
(3)
(4)
(5)
does not affect the capacitance
increases the capacitance
does not affect the potential difference
increases the potential difference
decreases the potential difference
14. A 15 Ω resistor and a 16 µF capacitor are connected in series to a 12 V battery. At t = 0.6 msec after the connection is
made, what is the current in the circuit?
(1) 0.80 A
(2) 1.25 A
(3) 0.25 A
(4) 0 A
(5) 0.066 A
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15. A battery is used to charge a series combination of two identical capacitors. If the potential difference across the battery
terminals is V and total charge Q flows through the battery during the charging process then the charge on the positive
plate of each capacitor and the potential difference across each capacitor are:
(1) Q and 2V
(2) Q/2 and V
(3) Q/2 and V /2
(4) Q and V
16. The light bulbs in the two diagrams are all identical. If the battery in Figure
A has an emf of 10.0 V, what should be the emf of the battery in Figure B so
that the total brightness or power of the light bulbs in Figure B is the same
as the total brightness or power of the bulbs in Figure A?
(5) Q and V /2
A
B
(1) 10.0 V
(2) 7.1 V
(3) 5.0 V
(4) 14.1 V
(5) 20.0 V
17. A straight wire has current flowing from the point, (x, y, z) = (2, 1, 0), to the point (x, y, z) = (1, 2, 0), where all positions
are measured in meters. The current is i = 2A. If a magnetic field is pointing in the z-direction of magnitude 5 T,
~ = 5T k̂, what is the force on the wire?
B
(1) (10î + 10ĵ)N
(2) (10î + −10ĵ)N
(3) (20î − 10ĵ)N
(4) (−10î + 10ĵ)N
(5) (−10î + 20ĵ)N
18. Three long wires have current flowing perpendicular to the page with directions
indicated in the figure. Wire 2 is located at the origin, wire 3 is at x = 2 m
on the x-axis, and wire 1 is at y = 2 m on the y-axis. If i1 = 1A, i2 = 2A,
i3 = 3A, what is the magnitude of the force per unit length on wire 2 due to
the other two wires?
(1) 5.1 × 10−7 N/m
(2) 7.5 × 10−7 N/m
(3) 8.0 × 10−7 N/m
(4) 6.3 × 10−7 N/m
(5) 4.0 × 10−7 N/m
19. A uniform magnetic field is going into the plane of the page. Two charge
particles move in circles in the plane of the page as shown in the figure. The
two particles have the same magnitude of charge, |q|, and the same kinetic
energy. Which of the following is true about the particles’ charges and masses?
(1) q1 > 0, m1 > m2
(2) q1 < 0, m1 < m2
(3) q1 < 0, m1 = m2
(4) q1 < 0, m1 > m2
(5) q1 > 0, m1 < m2
20. A galvanometer with resistance 50 Ω measures a full-scale deflection when a current of 1 mA passes through the coil.
What value of the auxilliary resistance is required to convert the galvanomenter to a voltmeter that reads 1.5 V at
full-scale deflection.
(1) 150 Ω
(2) 100 Ω
(3) 1550 Ω
(4) 1500 Ω
(5) 1450 Ω